Prep the produce. Dice onion, carrots, and celery. Mince garlic. Pat chicken dry and season both sides with a pinch of salt and pepper.
Warm a large pot over medium heat. Add olive oil. Sauté onion, carrots, and celery for 5–6 minutes until slightly soft. Stir in garlic and thyme; cook 30 seconds until fragrant.
Add broth, bay leaf, and any optional boosters (like a parmesan rind). Stir and bring to a gentle boil.
Add the chicken to the pot. Reduce heat to a simmer. Cover partially and cook 12–18 minutes, until the chicken is just cooked through (internal temp 165°F / 74°C).
Transfer chicken to a plate. Shred with two forks. Skim any excess fat from the soup surface if you like.
If adding noodles, rice, or potatoes, stir them into the simmering broth and cook over medium-low heat until tender (noodles 6–8 minutes; rice 12–15; potatoes 10–12). Return shredded chicken to the pot. Add lemon juice.
Turn off heat. Stir in parsley. Taste and adjust salt and pepper. Remove bay leaf (and parmesan rind, if used). Ladle into bowls and serve warm.
Notes
For a rich flavor, use thighs or rotisserie chicken. Store noodles separately if freezing.